Purpose of Unit:
The purpose of this particular unit is to introduce students to 2-Dimensional kinematics. 2-Dimensional kinematics is oftentimes referred to as "Projectile Motion". This unit is intended for an introductory Junior or senior level high school physics course. Prior to beginning this unit, students should have already been exposed the concepts of position, velocity, acceleration, vectors and gravity. They should have already studied 1-dimensional kinematics and should be able to analyze the motion of an object moving horizontally or vertically. The concepts and techniques used to solve problems involving objects in free fall and objects moving horizontally are very similar to those implemented within the projectile motion unit. Students should be familiar with the 3 major kinematics equations and should have a strong enough mathematical background to isolate variables of a given equation and solve systems of equations involving 2 unknowns. They should also be familiar with the various steps to problem solving. They should be proficient at extracting information presented in a word problem and applying the appropriate formulas to arrive at the correct answer. This unit will help students to extend their knowledge of objects in motion and will enable them to analyze the motion of an object that is projected/ moving in both the x and the y directions.
This unit is also designed to help students discover how the physical concepts that they are learning directly relate to their own lives outside of the classroom. They will apply their knowledge of projectile motion to real world applications and will be given the opportunity to see how applicable projectile motion can be to the real world. This unit is also designed to improve the problem solving and critical thinking skills of the students. They will be confronted with unfamiliar problems and will have to use various problem-solving strategies in order to come up with an original way to reach a conclusion.
The purpose of this unit is thus two-fold; it serves to acquaint students with the concepts of projectile motion as well as helping them develop problem solving and critical thinking skills.
Note: This unit is designed to be taught in a school that has 90-minute “block” periods. The lessons are designed for this amount of time but could always be split into 2 pieces in order to work for a schedule with shorter blocks.
Unit Rationale:
Projectile motion can be applied to many different areas of our lives and there are so many examples of projectiles that we all see in the world around us each and every day. I designed this unit so that students will understand that what they are learning about is applicable in the real world. They will be exposed to the many different examples of projectile motion and they will be able to solve problems that relate to real world situations and athletic maneuvers. This parallels nicely with my teaching philosophy because one of my main concerns as a physics teacher is to help the students connect what they are learning to what they experience outside of the walls of the classroom.
I also designed this unit so that it includes several inquiry-based activities. The students will be given the opportunity to design and implement their own procedures in order to solve a problem that I will present to them. I will restrict the materials that they are allowed to use and they must determine a way in which they can find the desired results. These activities will help to develop the students' critical thinking and problem solving skills which I think are incredibly important skills for students to have. The students will develop their ability to define a problem, formulate a hypothesis, design an investigation, implement an investigation, and interpret the results through the activities that we will perform throughout this unit. These inquiry activities also parallel with my teaching philosophy because students are given an opportunity to explore and discover physical concepts on their own without me explicitly teaching them.
Finally, I included a great deal of group work within this unit because I think that working cooperatively is something that all students need to learn. I give them the opportunity to work together in order to reach a common goal and I let them discuss issues amongst themselves in order to arrive at the correct result. I considered these ideas as I designed this unit plan from the ground up and I am very pleased with the result.
Unit Summary:
The first two lessons of this unit are designed to prepare the students for the heart of the unit and projectile motion is not introduced until the third lesson. The first lesson is entirely a lesson in mathematics and focuses on introducing the students to the basic trigonometric ratios. They will learn how to use these ratios to find components of a given vector in the x and y directions. This knowledge is essential for students to have before beginning the unit on projectile motion because without it they will not be able to treat the x and y directions separately in order to solve 2D kinematics problems. In the second lesson 1D kinematics will be thoroughly reviewed with the students. They will review the 3 major kinematics equations and will be presented with problems involving objects in free fall and objects moving horizontally. The techniques used to solve projectile motion problems is very similar to that used in 1D kinematics problems and I want to ensure that students are proficient with 1D problems before moving on to the more challenging 2D problems.
The third lesson serves as the introduction to projectile motion for the students. Students will be exposed to the bullet shot/ bullet dropped theory which will introduce them to the perplexing idea that an objects motion in the x direction is independent of its motion in the y direction. Following this they will develop a "mini" investigation to test out this theory. They will have to develop their own procedure to test this idea and will implement it using materials that I will provide to them. In lesson #4 students will discuss the results of the investigation from the third lesson and they will then be introduced to the basic concepts involved in projectile motion. There will be a brief note taking session in which students will see how the knowledge that they learned in the 1D kinematics unit can be applied to 2D kinematics as well. Several example problems will be assigned in order to give students experience with kinematics problems. In lesson #5 students will be given the opportunity to apply basic 2D kinematics procedures to a computer simulation that is run by the University of Colorado. This allows them to apply their knowledge of projectile motion to a real world application that they can manipulate using the computer program.
Lesson #6 &7 involve the students designing their own investigation in order to determine how far/ how fast they can throw a baseball or bick a soccer ball. They will have to design and implement their own procedures in order to achieve the desired results. This is a great student centered inquiry learning activity. The final two lessons of the unit involve more practice problems for the students to complete and they will also be required to formulate their own projectile motion problems in groups. This unit will expose students to a variety of different projectile motion problems that they may see in the future on AP examinations. The short form lesson plans for each of the lessons can be seen immediately below and the long form plans can be seen on the proceeding pages.
Unit Plan Goals:
i. Students should understand how 1D kinematics principles and equations can be applied to objects moving in both the x and the y directions.
ii. Students should be able to apply their knowledge of projectile motion to calculate the range, time of flight, and maximum height of projectiles launched at an angle to the horizontal.
iii. Students should be able to apply their problem solving strategies to dissect kinematics word problems and accurately solve them.
iv. Students should conceptually understand and be able to explain in detail the “bullet shot/ bullet dropped” theory.
v. Students will refine their skills in developing and implementing scientific investigations. They will also learn how to interpret data that is collected.
Guiding Questions:
i. Why do a bullet shot and a bullet dropped from the same height at the same time reach the ground simultaneously?
ii. What does it mean for the motion of an object in the x and y directions to be independent? How does this help us to solve projectile motion problems?
iii. How can we calculate the range of a projectile using basic kinematics equations?
iv. What are the steps to problem solving?
Assessment Plan:
Throughout this unit, I implement several different forms of assessment including informal and formal assessments. The main form of assessment that resonates throughout all of the lessons is informal assessment. I will constantly be observing the students and determining whether or not they are truly understanding the concepts being taught. My main concern is that all of my students conceptualize what they are being taught and meaningfully learn it. I will monitor their progress throughout the unit and make necessary adjustments to my instruction to accommodate for any students that may be falling behind and those that may not be challenged enough (these accommodations are discussed in detail in the following lesson plans).
In addition to the informal assessments that I will make along the way I also will be collecting and formally grading several in class assignments and quizzes. These assignments will also allow me to gauge how well each student understands projectile motion. Finally, the overall assessment that will be given at the end of the unit is a written examination that will be completed independently by each of the students. The last two lessons will be spent reviewing various kinematics problems and concepts so students should be well prepared for the written exam. This formal assessment will certainly test the students on how well the understand projectile motion and on how well they can apply their problem solving skills to solve real world problems.
Standards Addressed: I. MATH GSEs: Grade Span Expectations [Math]: M(N&O)–10–8 Applies properties of numbers to solve problems, to simplify computations, or to compare and contrast the properties of numbers and number systems. M(F&A)–10–1 Identifies, extends, and generalizes a variety of patterns (linear and nonlinear) represented by models, tables, sequences, or graphs to solve problems. M(PRP)–HS–1 Students will use problem-solving strategies to investigate and understand increasingly complex mathematical content and be able to:
• Expand the repertoire of problem-solving strategies and use those strategies in more sophisticated ways.
• Use technology whenever appropriate to solve real-world problems (e.g., personal finance, wages, banking and credit, home improvement problems, measurement, taxes, business situations, purchasing, and transportation).
• Formulate and redefine problem situations as needed to arrive at appropriate conclusions. II. Physics GSEs: Grade Span Expectations [Physics]: PS3 (7-8) 8: Students demonstrate and understanding of motion by… (8a)… measuring the distance and time for a given moving object and using those values to calculate speed. (8b)… Solving for any unknown in the expression v=d/t given values for the other two variables. (8c)… Differentiating between speed, velocity and acceleration.
PS3 (9-11) 8: Students demonstrate and understanding of forces and motion by… (8a)… Predicting and/or graphing the path of an object in different reference planes and explain how and why it occurs. (8b)… Using modeling, illustrating, and graphing to explain how distance and velocity change over time for a free falling object.
PS3 (Ext) 8: Students demonstrate an understanding of forces and motion by… (8aa)… Using a quantitative representation of how distance and velocity change over time for a free falling object. (8bb)… Using a quantitative representation of the path of an object that has both horizontal and free fall motion. (8cc)… Modeling, illustrating, graphing, and or quantitatively explaining the path of an object that has both horizontal and free fall motion.
Student investigation into the trigonometric ratios
Right triangles
SOHCAHTOA explained
HW practice problems.
Objectives:
Students will demonstrate their understanding of basic trigonometric ratios by successfully determining how the sine, cosine, and tangent of a given acute angle of a right triangle are related to the sides of the triangle.
Students will demonstrate their understanding of the relationships that exist between the angles and sides of a right triangle by successfully splitting “vectors” into their horizontal and vertical components and following navigation directions on the football field.
Lesson Summary:
Projectile motion requires students to work with 2D velocity vectors and they must be able to “break” these vectors into x and y components. In order to do this, students need to have an understanding on basic trigonometric ratios related to an acute angle of a right triangle. This lesson is designed to allow students to discover the trigonometric ratios for sine, cosine, and tangent on their own by investigating various right triangles and analyzing the relationship that the sides of the given triangle have with the sine, cosine, and tangent of one of the acute angles within the triangle. The students will also apply this knowledge to a second activity in which they are asked follow (displacement vectors) directions on the football. Students will be given a set of directions on where to walk from a given starting point on the football field and they must break the displacement vectors into x and y components because they will not be provided with a protractor. This activity will be a great way to ensure that students can find the components of a given vector.
Assessment: Students will be informally assessed and I will gauge the students’ understanding of the material and determine whether the unit can move forward
Materials Needed:
Attached worksheets. Details in lesson plan
10 envelopes with sets of “directions” for students to follow. Teacher should calculate ahead of time where each “set” will end up on the field.
Lesson 2: Review of 1D Kinematics and Objects in Free Fall Key Factors:
Begin with short quiz on breaking components into vectors
Short instructional session on concepts that were learned in the previous unit
Review of kinematics equations that were used in the 1D case
Students will break into groups to work on problems associated with 1D motion and objects in free fall
Groups will present one problem and explain reasoning
Objectives:
Students will demonstrate their understanding of 1-Dimensional kinematics and objects in free fall by successfully completing 5 problems, which deal with these concepts.
Lesson Summary:
Prior to the projectile motion unit, students will have studied 1D motion and will have been exposed to the kinematics equations that govern such situations. Students will have also been exposed to the idea of the acceleration due to gravity and will be able to analyze the motion of objects in free fall. Since these concepts will be critical in the projectile motion unit, I want to use a class period to review these ideas and make sure that everyone is ready to put it all to get and analyze motion in 2 dimensions. This lesson will be a review of these concepts. I will begin the lesson by creating small “game” with various conceptual questions to ask the students. This will help us review the concepts. I will then remind the students of the kinematics equations for 1 dimensional motion and I will have them break up into groups to work on several problems. There will be four stations in the room each with 2 problems. The groups will circulate the room and work on these problems. At the end of the day each group will present on of the problems and will explain their thought process to the class.
Assessment: Students will be formally assessed with a quiz on their ability to break vectors into components at the beginning of the lesson. They will then be informally assessed on their understanding of 1 dimensional motion and objects in free fall. I will gauge their understanding and be sure to develop this foundation before we proceed with the unit.
Materials Needed:
10 problems relating to 1D motion and objects in free fall.
Game involving concepts from 1D motion
Homework assignment for further review.
Lesson 3: Independent Directions: Mini Lab!
Key Factors:
Discover that for the motion of a projectile, the x and y directions are completely independent
Introduction to projectile motion, examples of projectiles shown (sports, hunting, parachuting, etc)
Short video clip of myth-busters episode (Bullet shot vs. bullet dropped).
Students design mini lab to test this theory!
Objectives:
Students will design and implement an investigation in which they successfully find experimental support of the fact that motion in the x and y directions are independent of one another.
Lesson Summary:
A major concept involved in projectile motion has to do with the fact that an objects motion in the x direction is essentially unrelated to the objects motion in the y direction. In other words an object that is shot horizontally from a given height above the ground will reach the ground at the same time as an object that is simultaneously dropped from that same height. This idea is fundamental for all projectile motion problems and it is essential that the students understand this. I will show a myth-busters video that is related to this idea and students will design an experiment to test it out.
Assessment: Students will be informally assessed during the investigation on their ability to create and implement a scientific investigation using the scientific method. I will gauge the students’ understanding of this concept during the investigation.
Materials Needed:
Myth-Busters video clip
Elastic bands, small balls/projectiles, timers/ stopwatches.
Lesson 4: Introduction to Projectile Motion
Key Factors:
Discussion and presentation of results from previous day.
Implications of results!
Presentation of equations used in 2 dimensions
Review of procedure used to solve problems (graphic organizer)… split directions
In class examples
HW practice problems assigned.
Objective:
Students will demonstrate their understanding of how projectile motion problems are solved by successfully completing several example problems.
Lesson Summary:
During this lesson we will review the results of the investigation that was performed the day before. Each group will present their results to the class and explain the procedure that they followed. Once the results have been shared we will talk about the implications of this idea. We will then have a short note-taking session in which I present the 2 dimensional kinematics equations that they will need to be familiar with in order to successfully solve kinematics problems. I will then model an example problem and stress the “process” and steps that I took to solve it. They will be given the opportunity to work on simple projectile motion problems together as a class.
Assessment: Students will be informally assessed on their ability to complete the second problem in groups. I will gauge the students’ understanding of the material and determine whether the unit can move forward.
Materials Needed:
Small whiteboards for groups to record their results
3 example problems on basic 2D motion.
Lesson 5: Projectile Motion: A Student Investigation.
Key Factors:
Derivation of “Range” equation.
Computer application from university of California used for projectile motion.
Students will work together in groups to answer several questions regarding projectiles launched.
They can launch the projectiles using computer program to test their answers.
Objectives:
Students will successfully apply the scientific method in order to develop an original procedure for calculating the initial velocity of projectile using specific materials.
Students will successfully implement their original scientific procedure and will quantitatively calculate the initial velocity with which they can throw a projectile.
Lesson Summary:
During this lesson I will have the students break up into groups of two. They will be required to complete a short assignment that involves using a computer program that was created at the University of Colorado. This computer program allows students to shoot projectiles from various initial heights at various angles and determine where it should land. For various situations students will need to do out their calculations to calculate the range of the projectile and then use the computer software to check their answers. They can also experiment with the program to optimize the range of the projectile and perform other inquirybased activities. We will conclude the class by discussing the results and I will derive the range equation for them.
Assessment: The in class assignment will be collected and will count as a quiz grade. Students will therefore be formally assessed during this lesson on their understanding of projectile motion and on how to apply what they learned to real world applications
Materials Needed:
Computers/ Laptops
Assignment sheet with guiding questions
Lesson 6&7:Projectile Motion: How fast?
Key Factors:
Students will determine how fast they can throw/kick by using projectile motion kinematics
The will only be able to have a slow motion camera and a measuring tape. No timer!
Students will work in groups in order to develop a technique and will present this technique to class prior to the activity.
Done on the football field
Objectives:
Students will demonstrate their understanding of projectile motion by successfully determining how fast they can throw a baseball using kinematics techniques.
Students will successfully use the scientific method to develop an effective procedure for determining the initial velocity of an object.
Lesson Summary:
On day one of this investigation I will explain to the students that I want them to determine how fast they can throw a baseball and or kick a soccer ball. The students will spend time in their groups discussing different strategies regarding how this can be done. I want each group to come up with two different strategies and develop a plan for how they can carry out these procedures. They will then present their proposed procedure to the class and we will discuss the different ideas. Each group will finalize their plans and write up the final procedure and we will prepare the materials for the next day. On day 2 they will implement their plans and will each use 2 different methods to determine how fast they can throw and or kick a ball. We will discuss the results as a class and talk about how it fits in to the projectile motion unit.
Assessment: Students will turn in their work (mini lab report) and will be formally assessed on their ability to use the scientific method and perform the necessary calculations.
Materials Needed:
Measuring tapes
Cameras slow motion. Or video cameras
Worksheet for investigation
Lesson 8: Projectile Motion: A Student Challenge
Key Factors:
Problem session
Group work
10 questions/ 4 stations
Each group presents 1 problem of their choice to the class.
Objectives:
Students will demonstrate their understanding of projectile motion by successfully solving several problems.
Lesson Summary:
I will have developed 10 different multi part problems and I will create 5 different stations with 2 questions at each station. In groups the students will rotate between the stations and complete the problems. There will be a visual representation (picture of model) of each problem at each of the stations. At the end of the class period each of the groups will choose one of the problems to present and they will talk to the class about the process and the methods that they used to solve the problems. All solutions will be handed in at the end of the class and the students will receive a quiz grade for their work.
Assessment: Students will be formally assessed on their knowledge of projectile motion. Their work will be passed in at the end of the class and I will grade it on completeness and accuracy.
Materials Needed:
10 different problems.
Visual representations of all problems (pictures and models)
Lesson 9: It's your turn!
Key Factors:
Students will break up into groups
Develop questions on their own for their classmates to answer
Jigsaw!1
Problem session
Objectives:
Students will demonstrate their understanding of projectile motion by successfully developing questions/problems for their classmates.
Lesson Summary:
During this lesson students will break up into groups and they will develop their own multi-part projectile motion problems. They will invent a scenario and try to make a difficult problem for their peers to solve. They will draw a diagram and type up their questions. The groups will then all change and no members will be in the same group. They will swap problems and will have to solve everyone else’s.
Assessment: Students will be informally assessed and I will gauge the students’ understanding of the material and determine whether the unit can move forward.
2-Dimensional Kinematics
Purpose of Unit:
The purpose of this particular unit is to introduce students to 2-Dimensional kinematics. 2-Dimensional kinematics is oftentimes referred to as "Projectile Motion". This unit is intended for an introductory Junior or senior level high school physics course. Prior to beginning this unit, students should have already been exposed the concepts of position, velocity, acceleration, vectors and gravity. They should have already studied 1-dimensional kinematics and should be able to analyze the motion of an object moving horizontally or vertically. The concepts and techniques used to solve problems involving objects in free fall and objects moving horizontally are very similar to those implemented within the projectile motion unit. Students should be familiar with the 3 major kinematics equations and should have a strong enough mathematical background to isolate variables of a given equation and solve systems of equations involving 2 unknowns. They should also be familiar with the various steps to problem solving. They should be proficient at extracting information presented in a word problem and applying the appropriate formulas to arrive at the correct answer. This unit will help students to extend their knowledge of objects in motion and will enable them to analyze the motion of an object that is projected/ moving in both the x and the y directions.
This unit is also designed to help students discover how the physical concepts that they are learning directly relate to their own lives outside of the classroom. They will apply their knowledge of projectile motion to real world applications and will be given the opportunity to see how applicable projectile motion can be to the real world. This unit is also designed to improve the problem solving and critical thinking skills of the students. They will be confronted with unfamiliar problems and will have to use various problem-solving strategies in order to come up with an original way to reach a conclusion.
The purpose of this unit is thus two-fold; it serves to acquaint students with the concepts of projectile motion as well as helping them develop problem solving and critical thinking skills.
Note: This unit is designed to be taught in a school that has 90-minute “block” periods. The lessons are designed for this amount of time but could always be split into 2 pieces in order to work for a schedule with shorter blocks.
Unit Rationale:
Projectile motion can be applied to many different areas of our lives and there are so many examples of projectiles that we all see in the world around us each and every day. I designed this unit so that students will understand that what they are learning about is applicable in the real world. They will be exposed to the many different examples of projectile motion and they will be able to solve problems that relate to real world situations and athletic maneuvers. This parallels nicely with my teaching philosophy because one of my main concerns as a physics teacher is to help the students connect what they are learning to what they experience outside of the walls of the classroom.
I also designed this unit so that it includes several inquiry-based activities. The students will be given the opportunity to design and implement their own procedures in order to solve a problem that I will present to them. I will restrict the materials that they are allowed to use and they must determine a way in which they can find the desired results. These activities will help to develop the students' critical thinking and problem solving skills which I think are incredibly important skills for students to have. The students will develop their ability to define a problem, formulate a hypothesis, design an investigation, implement an investigation, and interpret the results through the activities that we will perform throughout this unit. These inquiry activities also parallel with my teaching philosophy because students are given an opportunity to explore and discover physical concepts on their own without me explicitly teaching them.
Finally, I included a great deal of group work within this unit because I think that working cooperatively is something that all students need to learn. I give them the opportunity to work together in order to reach a common goal and I let them discuss issues amongst themselves in order to arrive at the correct result. I considered these ideas as I designed this unit plan from the ground up and I am very pleased with the result.
Unit Summary:
The first two lessons of this unit are designed to prepare the students for the heart of the unit and projectile motion is not introduced until the third lesson. The first lesson is entirely a lesson in mathematics and focuses on introducing the students to the basic trigonometric ratios. They will learn how to use these ratios to find components of a given vector in the x and y directions. This knowledge is essential for students to have before beginning the unit on projectile motion because without it they will not be able to treat the x and y directions separately in order to solve 2D kinematics problems. In the second lesson 1D kinematics will be thoroughly reviewed with the students. They will review the 3 major kinematics equations and will be presented with problems involving objects in free fall and objects moving horizontally. The techniques used to solve projectile motion problems is very similar to that used in 1D kinematics problems and I want to ensure that students are proficient with 1D problems before moving on to the more challenging 2D problems.
The third lesson serves as the introduction to projectile motion for the students. Students will be exposed to the bullet shot/ bullet dropped theory which will introduce them to the perplexing idea that an objects motion in the x direction is independent of its motion in the y direction. Following this they will develop a "mini" investigation to test out this theory. They will have to develop their own procedure to test this idea and will implement it using materials that I will provide to them. In lesson #4 students will discuss the results of the investigation from the third lesson and they will then be introduced to the basic concepts involved in projectile motion. There will be a brief note taking session in which students will see how the knowledge that they learned in the 1D kinematics unit can be applied to 2D kinematics as well. Several example problems will be assigned in order to give students experience with kinematics problems. In lesson #5 students will be given the opportunity to apply basic 2D kinematics procedures to a computer simulation that is run by the University of Colorado. This allows them to apply their knowledge of projectile motion to a real world application that they can manipulate using the computer program.
Lesson #6 &7 involve the students designing their own investigation in order to determine how far/ how fast they can throw a baseball or bick a soccer ball. They will have to design and implement their own procedures in order to achieve the desired results. This is a great student centered inquiry learning activity. The final two lessons of the unit involve more practice problems for the students to complete and they will also be required to formulate their own projectile motion problems in groups. This unit will expose students to a variety of different projectile motion problems that they may see in the future on AP examinations. The short form lesson plans for each of the lessons can be seen immediately below and the long form plans can be seen on the proceeding pages.
Unit Plan Goals:
i. Students should understand how 1D kinematics principles and equations can be applied to objects moving in both the x and the y directions.
ii. Students should be able to apply their knowledge of projectile motion to calculate the range, time of flight, and maximum height of projectiles launched at an angle to the horizontal.
iii. Students should be able to apply their problem solving strategies to dissect kinematics word problems and accurately solve them.
iv. Students should conceptually understand and be able to explain in detail the “bullet shot/ bullet dropped” theory.
v. Students will refine their skills in developing and implementing scientific investigations. They will also learn how to interpret data that is collected.
Guiding Questions:
i. Why do a bullet shot and a bullet dropped from the same height at the same time reach the ground simultaneously?
ii. What does it mean for the motion of an object in the x and y directions to be independent? How does this help us to solve projectile motion problems?
iii. How can we calculate the range of a projectile using basic kinematics equations?
iv. What are the steps to problem solving?
Assessment Plan:
Throughout this unit, I implement several different forms of assessment including informal and formal assessments. The main form of assessment that resonates throughout all of the lessons is informal assessment. I will constantly be observing the students and determining whether or not they are truly understanding the concepts being taught. My main concern is that all of my students conceptualize what they are being taught and meaningfully learn it. I will monitor their progress throughout the unit and make necessary adjustments to my instruction to accommodate for any students that may be falling behind and those that may not be challenged enough (these accommodations are discussed in detail in the following lesson plans).
In addition to the informal assessments that I will make along the way I also will be collecting and formally grading several in class assignments and quizzes. These assignments will also allow me to gauge how well each student understands projectile motion. Finally, the overall assessment that will be given at the end of the unit is a written examination that will be completed independently by each of the students. The last two lessons will be spent reviewing various kinematics problems and concepts so students should be well prepared for the written exam. This formal assessment will certainly test the students on how well the understand projectile motion and on how well they can apply their problem solving skills to solve real world problems.
Standards Addressed:
I. MATH GSEs:
Grade Span Expectations [Math]:
M(N&O)–10–8 Applies properties of numbers to solve problems, to simplify computations, or to compare and contrast the properties of numbers and number systems.
M(F&A)–10–1 Identifies, extends, and generalizes a variety of patterns (linear and nonlinear) represented by models, tables, sequences, or graphs to solve problems.
M(PRP)–HS–1 Students will use problem-solving strategies to investigate and understand increasingly complex mathematical content and be able to:
• Expand the repertoire of problem-solving strategies and use those strategies in more sophisticated ways.
• Use technology whenever appropriate to solve real-world problems (e.g., personal finance, wages, banking and credit, home improvement problems, measurement, taxes, business situations, purchasing, and transportation).
• Formulate and redefine problem situations as needed to arrive at appropriate conclusions.
II. Physics GSEs:
Grade Span Expectations [Physics]:
PS3 (7-8) 8: Students demonstrate and understanding of motion by…
(8a)… measuring the distance and time for a given moving object and using those values to calculate speed.
(8b)… Solving for any unknown in the expression v=d/t given values for the other two variables.
(8c)… Differentiating between speed, velocity and acceleration.
PS3 (9-11) 8: Students demonstrate and understanding of forces and motion by…
(8a)… Predicting and/or graphing the path of an object in different reference planes and explain how and why it occurs.
(8b)… Using modeling, illustrating, and graphing to explain how distance and velocity change over time for a free falling object.
PS3 (Ext) 8: Students demonstrate an understanding of forces and motion by…
(8aa)… Using a quantitative representation of how distance and velocity change over time for a free falling object.
(8bb)… Using a quantitative representation of the path of an object that has both horizontal and free fall motion.
(8cc)… Modeling, illustrating, graphing, and or quantitatively explaining the path of an object that has both horizontal and free fall motion.
Lesson Sequence:
Lesson 1: Trigonometric Ratios
Lesson 2: 1D Kinematics Review
Lesson 3: Independent Directions Mini Lab
Lesson 4: Introduction to Projectile Motion
Lesson 5: PHET Projectile Motion Simulation
Lesson 6 & 7: How Fast
Lesson 8: A Student Challenge
Lesson 9: It's your turn!
Assessment: Projectile Motion Unit Exam
Unit Overview:
Lesson 1: Trigonometric Ratios
Key Factors:
Objectives:
Lesson Summary:
Assessment: Students will be informally assessed and I will gauge the students’ understanding of the material and determine whether the unit can move forward
Materials Needed:
Lesson 2: Review of 1D Kinematics and Objects in Free Fall
Key Factors:
Objectives:
Lesson Summary:
Assessment: Students will be formally assessed with a quiz on their ability to break vectors into components at the beginning of the lesson. They will then be informally assessed on their understanding of 1 dimensional motion and objects in free fall. I will gauge their understanding and be sure to develop this foundation before we proceed with the unit.
Materials Needed:
Lesson 3: Independent Directions: Mini Lab!
Key Factors:
Objectives:
Lesson Summary:
Assessment: Students will be informally assessed during the investigation on their ability to create and implement a scientific investigation using the scientific method. I will gauge the students’ understanding of this concept during the investigation.
Materials Needed:
Lesson 4: Introduction to Projectile Motion
Key Factors:
Objective:
Lesson Summary:
Assessment: Students will be informally assessed on their ability to complete the second problem in groups. I will gauge the students’ understanding of the material and determine whether the unit can move forward.
Materials Needed:
Lesson 5: Projectile Motion: A Student Investigation.
Key Factors:
Objectives:
Lesson Summary:
Assessment: The in class assignment will be collected and will count as a quiz grade. Students will therefore be formally assessed during this lesson on their understanding of projectile motion and on how to apply what they learned to real world applications
Materials Needed:
Lesson 6&7: Projectile Motion: How fast?
Key Factors:
Objectives:
Lesson Summary:
Assessment: Students will turn in their work (mini lab report) and will be formally assessed on their ability to use the scientific method and perform the necessary calculations.
Materials Needed:
Lesson 8: Projectile Motion: A Student Challenge
Key Factors:
Objectives:
Lesson Summary:
Assessment: Students will be formally assessed on their knowledge of projectile motion. Their work will be passed in at the end of the class and I will grade it on completeness and accuracy.
Materials Needed:
Lesson 9: It's your turn!
Key Factors:
Objectives:
Lesson Summary:
Assessment: Students will be informally assessed and I will gauge the students’ understanding of the material and determine whether the unit can move forward.
Materials Needed: